Case 2: A mitotic index that was asked to do too much
A student investigates mitosis in a root tip. She cuts the last 5 mm from a garlic root, stains it, squashes it under a cover slip and counts every cell she can see in one field of view at ×400 magnification. She records 240 cells: 7 in prophase, 4 in metaphase, 5 in anaphase, 2 in telophase, and the rest apparently in interphase. A second student repeats the work using tissue taken 5 mm further back from the tip and counts 180 cells, of which 2 are in mitosis. The first student writes in her report: 'The mitotic index of the root is 7.5%, so 7.5% of the root's cells divide every hour, which is why the root grows about 7.5% longer every hour.' The teacher asks her to check both halves of that sentence, and to say how confident she can be in a figure based on one field of view.
1. Calculate the mitotic index from the first student's data and explain what the separate stage counts add to the result.
Read the worked answer
Mitotic index = cells in mitosis ÷ total cells counted = (7 + 4 + 5 + 2) ÷ 240 = 18 ÷ 240 = 0.075, i.e. 7.5%.
Show the working, because credit is given for the method as well as the value.
The stage counts add two things:
- Relative duration of each stage. Prophase (7 cells) is the most frequently seen dividing stage and telophase (2 cells) the least. If cells are counted at random, the number in a stage is roughly proportional to how long that stage lasts, so prophase is the longest of the visible stages and telophase the shortest.
- A check on the quality of the count. Cells in interphase (222 of 240) must be recognisable and counted, otherwise the denominator is wrong; a student who counts only cells with visible chromosomes would calculate something closer to 100%.
The value 7.5% says nothing about how long a complete cell cycle takes - that requires timing, not counting.
2. Explain why the sample taken 5 mm behind the tip gave a much lower mitotic index, and what this shows about where a root grows.
Read the worked answer
The last 5 mm of the root contains the meristem, a region of small, thin-walled, undifferentiated cells that are still dividing actively - hence 7.5% of cells caught in mitosis.
Five millimetres further back lies the zone of elongation and differentiation. Most cells there have left the cell cycle, have vacuolated and elongated, and are specialising into xylem, phloem, root hair cells and other tissues. Only a few retain the ability to divide, so the mitotic index is low (2 ÷ 180 ≈ 1.1%).
This shows that cell division is concentrated at the tip, and that root growth in length comes from two processes acting just behind the tip: division in the meristem producing new cells, and elongation of those cells. A root treated with a substance that blocks mitosis would stop growing in length even though older tissues remain alive, which is a useful control idea. The result also explains why root tips, not older root tissue, are used to study mitosis.
3. Evaluate the statement: 'The mitotic index is 7.5%, so 7.5% of the root's cells divide every hour, which is why the root grows about 7.5% longer every hour.'
Read the worked answer
Both halves are wrong, and for different reasons.
'7.5% divide every hour' - a proportion is being treated as a rate. The mitotic index is a snapshot: the fraction of cells that happened to be in mitosis at the moment the slide was made. It tells you nothing about how long a cell cycle takes, so it cannot be converted into 'per hour'. To get a rate you would need timed observations, e.g. marking the root and measuring its length every hour, or repeated sampling to follow how quickly the proportion of dividing cells changes.
'Grows 7.5% longer every hour' - growth is not proportional to the mitotic index. Length increase depends mostly on cell elongation in the zone behind the tip, not on the number of dividing cells, and only the tip region divides while the whole root gets longer. A root can grow quickly with a modest mitotic index.
Sampling is also weak. One field of view, from one root, counted once: 18 dividing cells is a small number, and fields vary. Several randomly chosen fields from at least three roots, averaged, would be needed before quoting 7.5% as the root's mitotic index at all.